A precise Johnson-Cook (J-C) constitutive model is the foundation for precise calculation of finite-element simulation. In order to obtain the J-C constitutive model accurately for a new cast and forged alloy GH4198, an inverse identification of J-C constitutive model was proposed based on a genetic-particle swarm algorithm. Firstly, a quasi-static tensile test at different strain rates was conducted to determine the initial yield strength A, strain hardening coefficient B, and work hardening exponent n for the material's J-C model. Secondly, a new method for orthogonal cutting model was constructed based on the unequal division shear theory and considering the influence of tool edge radius. In order to obtain the strain-rate strengthening coefficient C and thermal softening coefficient m, an orthogonal cutting experiment was conducted. Finally, in order to validate the precision of the constitutive model, an orthogonal cutting thermo-mechanical coupling simulation model was established. Meanwhile, the sensitivity of J-C constitutive model parameters on simulation results was analyzed. The results indicate that the parameter m significantly affects chip morphology, and that the parameter C has a notable impact on the cutting force. This study addressed the issue of missing constitutive parameters for GH4198 and provided a theoretical reference for the optimization and identification of constitutive models for other aerospace materials.